Slab Design Flowchart2

for f <= 90 N/mmck

BENDING

Carry out checkto

L/d7.4.2 (2)

See separate flowchartCalculate

to 7.4.3

No crackingcheck required

CRACKING

Use Table 7.3

7.3.2 (2)

for bar spacingCheck A , min tos

See separate flowchart

As 0.13% 26%f /fctm yk

but not 1.5As &nDist 0.12% 0.2Asprov

>= >=>>= >=

9.2.1.1 9.3.1.1(1)

9.3.1.1(2)

Primary s 3h 400Secondary s 3.5h 450

(smaller near point loads)

<= <=<= <=

9.3.1.1 (3) (4)&

Concrete Stress BlockDesign stress = hfcd

where f = a f /g andcd cc ck c

h = 1 - (f -50)/200 <= 1 ck

l = 0.8 - (f -50)/400 <= 0.8ck

3.1.6 (1)

(3.21) & (3.22)

(3.19) & (3.20)

( )dx 4.0max -= d from (5.10)

( )[ ] dKKd

z c 95.0',min2112

£-+= g

( ) 0'' 2 ³-= KKfbdM ck

Design Formulae

ckfbd

MK

2=

÷ø

öçè

æ-=

2' max

2max x

dd

xK

c

l

g

l

( )''

'ddf

MAs

sc -=

yd

sc

yd f

fAs

zf

MMAs '

'+

-=

Steel Design Stress

f = f /g yd yk s

Fig 3.8

s

yk

sc

f

x

dxf

g£÷

ø

öçè

æ -=

'700

SHEAR

Construction overloador striking < 7 days?

Is h > 200 mm?

DEFLECTION

No

No

Yes

Yes

If V V no links,Rd,ct Ed

otherwise see beams.>=

Where

( ) dbffkdb

V wctdckl

c

wctRd 4.0100

18.03

1

, ³= rg

(6.2)

2200

1 £+=d

k 02.0£=db

As

w

llr

and (3.16)c

ctmctctd

ff

g

a7.0=

rdprEN 1992-1 (3 draft)

Concrete Stress BlockAs for Slabs

s ,L = 0.75d max

s ,T 0.75d 600 max

(9.6)

(9.8)= <=

For point loadnear support, use

or 6.2.2.5 6.2.3 (8)

Tee & Ell Beam Flowchart2

for f <= 90 N/mmck

BENDINGSteel Design Stress

As for Slabs

Treat as rectangularsection, substituting

b for b.f

Is M > M ?ORf

No

Yes

( )f

f

ORffb

bwbMM

-=

( )÷ø

öçè

æ-

-+÷÷

ø

öççè

æ-=

22

xd

M

MMhd

M

Mz

fff l

0' ³-= ORMMM

( )''

'ddf

MAs

sc -=

yd

sc

yd f

fAs

zf

MMAs '

'+

-=

As 0.13% 26%f /fctm yk

Ascrack

Part of top steel at supportsmust be spread acrossthe width of the flange

>= >=

>=As9.2.1.1

7.3.2 (2)

9.2.1.2 (2)

SHEAR

Compression & tension flangewidths to 5.3.2.1

At d from support face

maxcot

mins

A

zf

Vs

As

A sw

ywk

sEdswsw £=£q

g(6.7)

yk

ckwsw

f

fbs

A 08.0min =where (9.4) & (9.5)

ywk

swcdsw

f

bfs

A

2m ax

gn=and (6.9)

Process as SlabsSee separate flowchart

CRACKINGDEFLECTION

Use Table 7.3

for bar spacingSee separate flowchart

Check main steel tensile

force due to shear) at zcotq/2from support

T (d

Or use Shift Rule 6.2.3 (7)

Fig 9.2

z may betaken as 0.9d

Flange MOR ÷÷ø

öççè

æ-==

2

f

ffcdORf

hdhbfM h

( )max2

610211 x

dfb

MMdx

cdw

f£

úú

û

ù

êê

ë

é ---=

hl

( )[ ]wwffcdOR xbbbhzfM lh +-=

At support face

Ed

cdw

V

fzb nqqw =+= tancot (6.8)

÷ø

öçè

æ-=

2 5 016.0 c kf

n (6.5)where

5.22

4cot1

2

£-+

=£ww

q 6.2.3 (2)

2200

1 £+=d

k 02.0£=db

As

w

llrwhere

and (3.14)

( ) Edcdw

Rd Vfzb

V ³+

=qq

n

tancotmax, (6.8)

( ) dbffkdb

V wctdckl

c

wctRd 4.0100

18.03

1

, ³= rg

(6.2)

c

ctmctctd

ff

g

a7.0=

rdprEN 1992-1 (3 draft)

Rectangular ColumnsDesign Flowchart

Final design momentM = M + M Ed 0Ed 2

M >= MEd 02

(5.33)

First order momentM = M + M0Ed 0E imp

ImperfectionsM = q N.l /2imp i 0

whereq =(2/3<=2/ l<=1)/200i Ö

Joint stiffnessesAt each end, k = relative column stiffness

ie. EI/l / S(EI/l ), but assume 50%col beams

of beam stiffnesses to allow for crackingsimplification of 5.8.3.2 (3)

Slenderness ratiol = l /i 0

where i = radius of gyration ofsection (including reinforcement)

(5.14)

Curvature1/r = K . K .1/rr f 0

where 1/r = f /(0.45d.E )0 yd s

= f /103500d andyk

K = 1 + bf >= 1 f ef

(5.34)

(5.37)

Axial load correction factorK = (n - n)/(n - n ) <= 1 r u u bal

where n = N /(A .f )Ed c cd

n = 1 + wu

(5.36)

n may be taken as 0.4bal

Creep correctionf = fM / M ef 0Eqp 0Ed (5.19)

f from 3.1.3

Is f <= 2,M/N >= h

and l <= 75?

No checkneeded

Is eyb/exh<= 0.2or exh/eyb <= 0.2?

b = 0.35 + f /200 - l /150ck

k = 1f

Second order momentM = N e2 Ed 2

2where e = (1/r) l /c2 0

(5.33)

2c normally p unless constant M0E

Second order momentM = 02

Effective length (5.16)

þýü

îíì

÷÷ø

öççè

æ

++÷÷

ø

öççè

æ

++

++=

2

2

1

1

21

210

11.

11;101max.

k

k

k

k

kk

kkll

SLENDERNESS

BUCKLINGMOMENTS

BIAXIALBENDING

Is Column braced? No

No

No

No

Yes

Yes

Yes

YesIs l <= 25(w+0.9)(2 - M /M )?01 02

where w =A f /(A f )>=0.05s yd c cd

(from 5.8.3.1)

M and M to01 02

include any globalsecond order

effects

Equivalent end momentM = 0.6M + 0.4M >= 0.4M0E 02 01 02

where M >= M02 01 (5.32)

Determine Rebar and MRd

from N:M interaction chartsúû

ùêë

é÷ø

öçè

æ +÷ø

öçè

æ +=

3

15,2,

12

1110,1,7.0

nMin

nMaxnIfa p

y dsc dc

E d

fAfA

Nn

+=

.Let , then

ndRepeat all for 2 axis then check

1£÷÷

ø

ö

çç

è

æ+÷÷

ø

öççè

æa

Rdy

Edy

a

Rdx

Edx

M

M

M

M(5.39)

÷÷ø

öççè

æ

++÷÷

ø

öççè

æ

++=

2

2

1

10

45.01.

45.015.0

k

k

k

kll

Effective length (5.15)

rdprEN 1992-1 (3 draft)

may be taken as for internal columns for edge columns or

for corner columns

b1.151.4

1.5 6.4.3 (6)

Enhancement

factor b

Slab Punching Flowchart(rectangular columns)

Do adjacent spansdiffer by <= 25%?

c = column dim in direction of M.1

c = column width.2

c = column dim parallel to edge.x

c = column dim normal to edge.y

u = full control perimeter (2d locus from1

column face, allowing for holes as ).

u * = reduced control perimeter.1

d = (dx + dy)

6.4.2 (3)

(6.33)½

Internal Column

b = 1 + k MEd u /(VEd W ) 1 1

where, if c /c <= 1,1 2

k = 0.45 + 0.3(c /c - 0.5) >= 0.451 2

or if c /c > 1,1 2

k = 0.6 + 0.1(c /c - 1) <= 0.81 2

and to

(6.40)

Table 6.1

(6.42)

12

221

2

11 2164

2dcddccc

cW p++++=

Edge Column

where k is as internal column,but replace c /c with c /2c1 2 1 2

and to 1(6.46)

p a reW

uk

u

u

1

1

1

1

*+=b

22

121

2

11 84

4dcddccc

cW p++++=

( ) dcdcu p2,3min* 121 ++=

02.0. £= lylxl rrr No

No

No

Or

Yes

Yes

Yes

Shear Stress

Links

At Column FacevEd = bVEd/(u .d)0

(6.54)

Is vEd > 0.3fcd[1-fck/250]?

Is vEd > vRd,c ?

Increase h

Links not required

At Control PerimetervEd = bVEd/(u .d) 1 (6.39)

( ) ctdckl

c

cRd ffkv 4.010018.0 3/1

, ³= rg

(6.48)

( )e fy w d

cR dE d

r

sw

f

uvvS

A

,

1,

5.1

7 5.0-=

y w de fy w d fd

f £+=4

2 5 0,

where

Asw = total link area on 1stperimeter (at >=0.3d &<=0.5d)

Outer control perimeteru = V /(v d)out Ed Rd,c

(6.55)

Last link perimeter <= 1.5dfrom u (polygonal shape) out

stS <= 1.5d on 1t,max

and <= 2d on lastperimeter

y ktr

s w

fS

f c kS

A

.5.1

8.0m i n, =

(9.11)

Internal u = 2(c1+c2)0

Edge u min(cx+3d,cx+2cy)0 =

Corner u min(3d,cx+cy)0 =

6.4.5 (2)

Corner Column

(6.47) where*1

1

u

u=b

dc

dc

du p+÷ø

öçè

æ+÷

ø

öçè

æ=

2,5.1min

2,5.1min* 21

1

If e is towardsoutside, treat asinternal column

Min h = 200

rdprEN 1992-1 (3 draft)

Flexural Crack Width CalculationFlowchart (rectangular sections)M = full SLS moment

t = age at cracking in daysfs = maximum tension bar diameterS = maximum tension bar spacings = cement type coefficient 0.20 for rapid hardening high strength 0.25 for normal & rapid hardening 0.38 for slow hardening

MATERIALS

Concrete modulus 0.3

Ecm = 22[(fck+8)/10]

Modular ratio ae = Es /Ecm

Time factor,

Mean concrete strength at crackingf (t) = b (t).fcm cc cm

Average concrete tensile strengthIf f >50, f = 2.12ln(1+f /10)ck ct,eff cm,t

2/3otherwise, f 0.3(f - 8)ct,eff = cm,t

Table 3.1

(3.2)

úúû

ù

êêë

é

÷÷ø

öççè

æ-=

tstcc

281exp)(b

STRESSES

CRACKING

Neutral axis depth

Concrete stress

Stress in tension steel

( ) ( )úúû

ù

êêë

é÷ø

öçè

æ++-+--=

d

ddx eee

222'2'' rrarrarra

( )( )( )úû

ùêë

é ---+÷

ø

öçè

æ-

=

x

dxddAs

xd

bx

M

e

c

222 1

32a

s

÷ø

öçè

æ -=

x

xds ecass

Crack width W = s (e - e )k max sm cm

(7.8)

Effective tension area

and

7.3.4 (2)

( ) ( )úû

ùêë

é --=

2,

3,5.2min,

hxhdhA effc

effc

effpA

As

,

, =rAverage strain for crack width calculation

(7.9)

( )

s

s

s

effpe

effp

effct

s

cmsmEE

f

sra

rs

ee 6.0

14.0 ,

,

,

³

+-

=-Max final crack spacing, if spacing <=5c+2.5f

otherwise, s = 1.3(h-x)r,max

where k = 0.8 for high bond, otherwise 1.61

and c = cover

(7.12)

e f fpr

kcs

,

1m a x,

2 1 2 5.04.3

rf

+= (7.11)

rdprEN 1992-1 (3 draft)